I've done similar a few times, mainly trips involving NYC and SIN and left a bag at left luggage at LHR during my connection so I didn't lug my winter clothes and US purchases to Singapore and back.

Absolutely no problem, it's even simpler than you are thinking - check in as normal at Amsterdam (e.g. online if you are HBO) - no need to mention anything there and then just take the bags and your boarding pass if you have it to check in at London and ask them to check them in.

Allow a bit of time for the left luggage - inevitably I found a bit of a wait whilst the person/people in front made it all more complex than it needed to be!!